Summary: We study \(q\)-Laguerre multiple orthogonal polynomials. These polynomials are orthogonal with respect to \(q\)-analogues of Laguerre weight functions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained and their explicit representations are given. A high-order linear \textit{q}-difference equation with polynomial coefficients is deduced. Moreover, we obtain the nearest neighbor recurrence relation using a \textit{q}-analogue of the theorem 23.1.11 by \textit{M. E. H. Ismail} in [Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Paperback reprint of the 2005 original. Cambridge: Cambridge University Press (2009; Zbl 1172.42008)].